24-3 Number of Equations: N E = 9 Eq. 2-48 through Eq. 2-56 Number of Parameters: N P = 3 V R , k, α Degrees of freedom: N F = 14 – 9 = 5 Number of manipulated variables: N MV = 4 w 1 , w 2 , w 6 , w 8 Number of disturbance variables: N DV = 1 x 2 D Number of controlled variables: N CV = 4 x 4A , w 4 , V T , x 8 D b) Model 1: The first model is left in an intermediate form, i.e., not fully reduced, so the key equations for the units are more clearly identifiable. Also, such a model is easier to develop using traditional balance methods because not as much algebraic effort is expended in simplification. Models 2 and 3: Both of the reduced models are easier to simulate (fewer equations), yet contain all of the dynamic relations needed to simulate the plant. Model 3: The “holdups model” has the further advantage of being easier to analyze using a symbolic equation manipulator because of its more symmetric organization. Also, it requires one less parameter for its specification. c) Each model can be simulated using the equations given in Appendix E of the text. Models 2 and 3 are simulated using the differential equation editor (dee) in Matlab. An example can be found by typing dee at the command prompt. Step changes are made in the manipulated variables w 1 , w 2 , w 6 and w 8 and in disturbance variable x 2 D to illustrate the dynamics of the entire plant.

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